The Japan international opened his Manchester United account, scoring the only goal in his team's 1-0 friendly win over a Drogba and Anelka-less Shanghai Shenhua
United's new man got on the end of Bebe's assist to give United the lead, earning Man of the Match honours following the encounter at Shanghai Stadium.
"I think we had plenty of possession of the ball and Kagawa was involved in most of that," Sir Alex told MUTVafter the friendly.
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"He was man of the match and he deserved that. He took his goal quite well, although it was a deflection. It was good work by Bebe too, who set it up for him."
The goal was Kagawa's first since joining the Red Devils in June, following two seasons with Bundesliga title-holders Dortmund, in his second starting appearance of the team's pre-season tour.
"Kagawa has settled in well. He's going to be a really good player and he impressed tonight," the 70-year-old added.
"His awareness of receiving the ball, his speed in turning and how he attacks defenders is an asset to us."
Kagawa himself was reluctant to attach much meaning to the goal, which came in the 68th minute on a humid night in Shanghai.
"I'm happy that I scored, but we weren't playing against a top opponent," the Samurai Blue regular told Nikkan.
"It's going to take time [to get into form]. Once our internationals [such as Wayne Rooney and Nani] return, I'll be able to play at a higher level."